Subgradient methods with perturbations in network problems

We study the impact of perturbations on the convergence of the subgradient method for the dual problem in constrained convex optimisation. Perturbations are likely to be present in practical implementations of the subgradient method and can affect either the computation of a subgradient, the update of the dual variables, or both. In the context of networks, perturbations can be related to the exchange of network information, time varying channel conditions, discrete actions, etc. The analysis presented in this paper is general, and establishes the conditions under which the objective function will converge to the optimum asymptotically. With an example, we illustrate how the analysis can be applied to network flow problems where the intensity of the flows that arrive in the system changes over time.